Question: Find the ordered pair $(j,k)$ that satisfies the equations $5j-42k=1$ and $2k-j=3$.
Answer: We can multiply the second equation by 5, so that our equations are \begin{align*}
5j -42k &=1\text{, and} \\
-5j +10k &=15. \end{align*}Summing these equations gives $-32k=16$, so $k=-16/32=-1/2$. We substitute this value for $k$ into one of the equations to solve for $j$: \begin{align*}
2\left(\frac{-1}{2}\right)-j&=3 \quad \Rightarrow \\ j &= -4.
\end{align*}So the solution is $\boxed{(-4,-\frac{1}{2})}$.